Number of rooted planar trees in which no branch is identical to its adjacent neighbor.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =10a(6) =28a(7) =77a(8) =221a(9) =650a(10) =1951a(11) =5920a(12) =18211a(13) =56509a(14) =176919a(15) =557786a(16) =1769966a(17) =5647568a(18) =18110734a(19) =58335561a(20) =188658338a(21) =612337013a(22) =1994058293a(23) =6513153445a(24) =21332562178a(25) =70048092196a(26) =230550762108a(27) =760462920317